# sqpt01.f - Man Page

TESTING/LIN/sqpt01.f

## Synopsis

### Functions/Subroutines

real function sqpt01 (m, n, k, a, af, lda, tau, jpvt, work, lwork)
SQPT01

## Function/Subroutine Documentation

### real function sqpt01 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( * ) tau, integer, dimension( * ) jpvt, real, dimension( lwork ) work, integer lwork)

SQPT01

Purpose:

``` SQPT01 tests the QR-factorization with pivoting of a matrix A.  The
array AF contains the (possibly partial) QR-factorization of A, where
the upper triangle of AF(1:k,1:k) is a partial triangular factor,
the entries below the diagonal in the first k columns are the
Householder vectors, and the rest of AF contains a partially updated
matrix.

This function returns ||A*P - Q*R|| / ( ||norm(A)||*eps*max(M,N) )
where || . || is matrix one norm.```
Parameters

M

```          M is INTEGER
The number of rows of the matrices A and AF.```

N

```          N is INTEGER
The number of columns of the matrices A and AF.```

K

```          K is INTEGER
The number of columns of AF that have been reduced
to upper triangular form.```

A

```          A is REAL array, dimension (LDA, N)
The original matrix A.```

AF

```          AF is REAL array, dimension (LDA,N)
The (possibly partial) output of SGEQPF.  The upper triangle
of AF(1:k,1:k) is a partial triangular factor, the entries
below the diagonal in the first k columns are the Householder
vectors, and the rest of AF contains a partially updated
matrix.```

LDA

```          LDA is INTEGER
The leading dimension of the arrays A and AF.```

TAU

```          TAU is REAL array, dimension (K)
Details of the Householder transformations as returned by
SGEQPF.```

JPVT

```          JPVT is INTEGER array, dimension (N)
Pivot information as returned by SGEQPF.```

WORK

`          WORK is REAL array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The length of the array WORK.  LWORK >= M*N+N.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 119 of file sqpt01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sqpt01(3) is an alias of sqpt01.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK